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In [1]:
import pandas as pd
import numpy as np
import seaborn as sns
from sklearn.decomposition import PCA, FactorAnalysis, FastICA
from sklearn import preprocessing
import matplotlib.pyplot as plt
import os
%matplotlib inline

pd.set_option('display.max_columns', None)
In [2]:
df=pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data',na_values='?',
               header=None,index_col=0)#,names=['mpg','cylinders','displacement','horsepower','weight','acceleration','model_year','origin','car_name'])
df=df.loc[:,:5]
df=df.dropna(how='any')
df.head()
Out[2]:
1 2 3 4 5
0
1000025 5 1 1 1 2
1002945 5 4 4 5 7
1015425 3 1 1 1 2
1016277 6 8 8 1 3
1017023 4 1 1 3 2

因子分析

官方文档 http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.FactorAnalysis.html#sklearn.decomposition.FactorAnalysis

In [3]:
g = sns.PairGrid(df)
g.map_upper(plt.scatter)
g.map_lower(sns.kdeplot, cmap="Blues_d")
g.map_diag(sns.kdeplot, lw=3, legend=False);
In [4]:
df.corr(method='pearson')
Out[4]:
1 2 3 4 5
1 1.000000 0.644913 0.654589 0.486356 0.521816
2 0.644913 1.000000 0.906882 0.705582 0.751799
3 0.654589 0.906882 1.000000 0.683079 0.719668
4 0.486356 0.705582 0.683079 1.000000 0.599599
5 0.521816 0.751799 0.719668 0.599599 1.000000
In [5]:
pca = PCA(n_components=4, whiten=True)
newData = pca.fit(df)
pca.explained_variance_ratio_
Out[5]:
array([ 0.75145722,  0.10706531,  0.07473669,  0.04572444])

降维到2维

In [6]:
from sklearn.decomposition import FactorAnalysis
fa = FactorAnalysis(n_components=2)
fa.fit(df)
Out[6]:
FactorAnalysis(copy=True, iterated_power=3, max_iter=1000, n_components=2,
        noise_variance_init=None, random_state=0, svd_method='randomized',
        tol=0.01)
In [7]:
fa.components_
Out[7]:
array([[ 2.05616371,  2.9326412 ,  2.77918866,  2.07561344,  1.70915869],
       [ 1.52598373, -0.32478952, -0.16031331, -0.23864157, -0.17768097]])
In [8]:
fa.transform(df)
Out[8]:
array([[-0.61353969,  0.80677518],
       [ 0.41289838, -0.14374713],
       [-0.71980402,  0.04491978],
       ..., 
       [ 1.96321658, -1.51951873],
       [ 1.09312746, -1.22284334],
       [ 1.32629844, -1.37729879]])
In [9]:
newData = pd.DataFrame(fa.transform(df),index=df.index,columns=['f1','f2'])
df.join(newData).head()
Out[9]:
1 2 3 4 5 f1 f2
0
61634 5 4 3 1 2 0.089490 0.148386
63375 9 1 2 6 4 -0.151058 2.110066
76389 10 4 7 2 2 0.740309 1.827701
95719 6 10 10 10 8 2.182572 -1.319922
128059 1 1 1 1 2 -0.826068 -0.716936